The Cantor-Schröder-Bernstein Theorem
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This result is of capital theoretical and historical importance. The Cantor-Schröder-Bernstein Theorem is also known as the Schröder-Bernstein Theorem or even the Cantor-Bernstein Theorem. In this video we tell you what it consists of, why it is known by many names and we will apply it to solve the question of whether there are as many points in an interval as in a square. Almost nothing! We also extend its application to the cube. RECOMMENDED BIBLIOGRAPHY. In the work of Martin Gardner one can approach the concept of infinity if one is not too familiar with it. In particular in: 1. MATHEMATICAL CARNIVAL. Martin Gardner. Alianza Editorial ???? ➡️ https://amzn.to/34cjOHY Chapter 3 is dedicated to presenting the cardinals alef zero and alef one (the cardinal of the continuum if we accept the continuum hypothesis). The Cantor bijection discussed in this video also appears in: 2. WHEEL, LIFE, AND OTHER MATHEMATICAL AMUSEMENTS. Martin Gardner. Labor ???? ➡️https://amzn.to/2SqvRyE In chapter 4 “Alephs and superhuman tasks”. The video takes as a source another slightly more specialized reference, namely: 3. HISTORY OF TOPOLOGY. Edited by I. M James. North-Holland ???? ➡️https://amzn.to/2QU5GAg Chapter 1 written by T. Crilly and D-Johnson deals with the emergence of the topological theory of dimension and describes the history narrated in this video. For a more exhaustive reference on cardinality a good reference is the book: 4. HILBERT'S TENTH PROBLEM. AN INTRODUCTION TO LOGIC, NUMBER THEORY AND COMPUTABILITY. M. Ram Murty, Brandon Fodden. American Mathematical Society ???? ➡️https://amzn.to/34egLPt Chapter 1 “Cantor and Infinity” is a nice compendium (with exercises) on infinite cardinals. The links included in this bibliography are affiliate links. If you purchase any of the books through these links, we may receive a small commission from that sale. This WILL HELP ARCHIMEDES TUBE to continue, but this will have no effect on the price at which you buy it, which will be the same. If you liked the video, like and sub! :D http://bit.ly/ArchiSub ???? Follow us on Instagram! http://bit.ly/InstaSub ???? Twitter: / archimedestub WEB: https://www.archimedestub.com/ ???????? Very cool Math T-shirts ➡️https://www.camisetasdematematicas.com/ ???? Math Books ➡️ https://www.amazon.es/shop/archimedes...
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